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Identify the part of the circle given the equation. 11. x^(2)+(y+3)^(2)=81 center: ◻ ◻ area : ◻ (answer in terms of pi)

Identify the part of the circle given the equation.\newline1111. x2+(y+3)2=81 x^{2}+(y+3)^{2}=81 \newlinecenter: (□( \square ,□ \square )\newlinearea : □ \square (answer in terms of pi)

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Full solution

Q. Identify the part of the circle given the equation.\newline1111. x2+(y+3)2=81 x^{2}+(y+3)^{2}=81 \newlinecenter: (□( \square ,□ \square )\newlinearea : □ \square (answer in terms of pi)
  1. Identify Equation Form: Identify the standard form of the circle equation and compare it to the given equation.\newlineStandard form: (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2\newlineGiven equation: x2+(y+3)2=81x^2 + (y + 3)^2 = 81\newlineHere, h=0h = 0, k=−3k = -3, and r2=81r^2 = 81.
  2. Calculate Radius: Calculate the radius of the circle.\newlineSince r2=81r^2 = 81, r=81=9r = \sqrt{81} = 9.
  3. Calculate Area: Calculate the area of the circle using the radius.\newlineArea = π×r2=π×92=81π\pi \times r^2 = \pi \times 9^2 = 81\pi.

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